Holographic Dual of The Weak Gravity Conjecture

TL;DR

This paper explores the holographic dual of the Weak Gravity Conjecture, revealing that it imposes lower bounds on the number of colors in boundary gauge theories, with implications for the quark-gluon plasma.

Contribution

It establishes a holographic interpretation of the Weak Gravity Conjecture, linking it to bounds on the number of colors in boundary theories via gauge-gravity duality.

Findings

Classical Censorship restricts small numbers of colors in realistic models.

Weak Gravity Conjecture provides a potential resolution to these restrictions.

Lower bounds on the number of colors are estimated for quark-gluon plasma applications.

Abstract

The much-discussed \emph{Weak Gravity Conjecture} is interesting and important in both the asymptotically flat and the asymptotically AdS contexts. In the latter case, it is natural to ask what conditions it (and the closely related Cosmic Censorship principle) imposes, via gauge-gravity duality, on the boundary field theory. We find that these conditions take the form of lower bounds on the number of colours in this theory: that is, the WGC and Censorship might (depending on the actual sizes of the bounds) enforce the familiar holographic injunction that this number should be "large". We explicitly estimate lower bounds on this number in the case of the application of holography to the quark-gluon plasma produced in heavy ion collisions. We find that classical Censorship alone prohibits realistically small values for the number of colours, but that the WGC offers hope of resolving this problem.